The alarm was raised at 11.30 a.m. by members of the 21-year-old's hunting party.
According to Hans Ängquist, county spokesman at Östersund police, the female bear was with her two young cubs and attacked the man when his dog started barking at an elk during the hunt. The hunter fired off two shots during the attack, the first to try and scare off the bear.
The injured man was taken by ambulance to Östersund Hospital where his injuries are not said to be life threatening.
A tracking party was searching for the bear late Saturday afternoon, but Hans Ängquist said it was not certain that the bear would be put down. He told SVT that it depended whether it had been injured in the gunfire.